Mutual coherence function determination from a double point source propagating through a transversely and longitudinally inhomogeneous aero-optic turbulence layer.

The mutual coherence function (MCF) that results when a double point source illuminates a transversely and longitudinally inhomogeneous turbulence layer is considered. The analysis was carried out by (1) decomposition of the free-space MCF from the double point source into four separate interference terms, (2) calculation of the MCF that resulted from each of these terms when the optical wave that arose from these terms propagated through the inhomogeneous turbulence layer, and (3) addition of the solutions together to form the overall MCF solution of the optical system. The analysis was carried out in a transverse center-difference coordinate system. Two of the four terms were shown to vary rapidly in the center coordinate variables, and the other two were shown to vary rapidly in the difference coordinate variables. Because two of the terms showed rapid interference effects in the center coordinate variable and the other two in the difference coordinate variable, two different spatial-spectral algorithms were developed in the paper to analyze the MCF's that arose from each of the two types of rapid interference variation. The spatial-spectral MCF equations that arose from the analysis were solved numerically by the Lax-Wendroff finite-difference method. Several numerical plots of the center and difference interference MCF's that resulted when a double point source was incident upon a transversely inhomogeneous aero-optic layer were given. Plots of the variation of the interference MCF's with angular separation of the double point source are shown.